ultrafast microscopy captures the dynamics of bound...

Ultrafast microscopy captures the dynamics of bound excitons in

twisted bilayer van der Waals materials

Hiral Patela, Kyle T. Vogt

a, Lujie Huang

b,c, Jiwoong Park

b,c, Matt W. Graham*

a

a Oregon State University, Department of Physics, Corvallis, OR 97331, USA

b Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY 14853, USA c Cornell University, Department of Chemistry, Ithaca, NY 14853, USA

ABSTRACT

Stacking and twisting 2D van der Walls (vdW) materials can create unique electronic properties that are not accessible in

a single sheet of material. When two sheets of van der Waals material such as graphene are stacked in an off-axis angle,

in a twisted bilayer graphene (tBLG) configuration, electronic properties are modified from interlayer orbital

hybridization effects. For instance, in tBLG we can access both massless and massive chiral quasiparticles characteristics

of graphene and bilayer graphene, as well as angle tunable optical resonances that are not present in graphene or bilayer

graphene. In addition, first principle simulation predicts that upon optical resonant excitation of tBLG, bound exciton

formation is a possibility due to cancelation of exciton-continuum coupling from anti-symmetric superposition of

degenerate resonant transitions. In order to study possible bound exciton formation, we map out the electronic structure

of single grain tBLG using multi-photon transient absorption microscopy. Surprisingly, upon resonant optical

excitations, tBLG shows enhanced transient response with longer carrier lifetime compared to AB stacked bilayer

graphene. Further, we find that the origin of this unexpected optical response can be best explained by the presence of a

lower lying bound exciton state predicted by recent theoretical simulations. This suggests that tBLG is a novel 2D hybrid

material that enables the creation of strongly-bound excitons along-side highly-conductive continuum states. Recently,

the family of 2D vdW materials has grown appreciably. As such, there are countless possibilities for stacking and

twisting 2D vDw materials to produce similar interlayer electronic states for next generation optoelectronics.

Keywords: van der Waals materials, twisted bilayer, ultrafast microscopy, excitons

1. INTRODUCTION

The Physics of 2D van der Walls (vdW) materials and heterostructures is being intensely studied and developed.

Material properties of vdW materials change drastically as you go from 3D to 2D1,2

. Stacking and twisting 2D vdW

materials create further unique properties that are not accessible in a single material. Graphene is a 2D structure of

carbon atoms arranged in a hexagonal lattice with two-carbon atoms per unit cell1,2

. It is the thinnest yet the strongest

material in the world which is electrically and thermally conductive, elastic, and impermeable to gases3,4,

. Owing to the

linear dispersion relation, the charge carriers in single layer graphene show similarity to massless Dirac fermions5,6

. In

bilayer graphene, at very low energies, the charge carriers are known to be massive chiral quasiparticles with parabolic

dispersion relation7. While intrinsic bilayer graphene does not have a bandgap, the carrier density in bilayer graphene

can be changed by either doping or gating, which enables the electronic properties to be tuned1,8,9

.

In vdW materials, the interlayer distance, stacking type, and rotation angles give rise to the unique electronic, optical,

and mechanical properties. Fabrication of graphene with chemical vapor deposition (CVD) show that single layer

graphene is often produced with significant amounts of bilayer graphene that include tBLG10,11

. In tBLG, two graphene

layers are rotated by an arbitrary angle with respect to each other. The rotation angle can be determined using dark-filed

transmission electron microscopy (DF-TEM)12

. It has been shown that photoexcited electrons relax faster than e-h

separation timescale for both graphene and bilayer graphene making it prohibitive for highly efficient optoelectronics

applications13

. However, we recently discovered that slower relaxation rate may be possible in metallic tBLG due to its

unique band symmetry14,34

. This has been shown theoretical modelling of the e-h interactions, and the simulations

predict the existence of strongly-bound excitons in an otherwise metallic material tBLG14

. The existence of bound

excitons in tBLG opens up a new realm of optoelectronic applications. Beyond graphene, this mechanism for interlayer

bound exciton formation is very general and may hold exciting promise for other stacked, twisted 2D vdW materials14

.

*[email protected]; phone 1 541 737-4631; fax 1 541 737-1683; http://physics.oregonstate.edu/energetics/index.html

Keynote Paper

Ultrafast Bandgap Photonics II, edited by Michael K. Rafailov, Proc. of SPIE Vol. 10193, 101930V © 2017 SPIE · CCC code: 0277-786X/17/$18 · doi: 10.1117/12.2262003

Proc. of SPIE Vol. 10193 101930V-1

Downloaded From: http://proceedings.spiedigitallibrary.org/ on 05/17/2017 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx

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2. REVIEW OF THEORY: INTERLAYER ELECTRONIC STRUCTURE

2.1 Electronic band structure of graphene in the tight binding approximation

We begin with a brief review of the electronic structure of graphene to establish a common notation for discussing the

interlayer electronic structure of twisted bilayer graphene (tBLG) in the later sections. The atomic structure of single

layer graphene in Figure 1a shows distinct carbon atoms, A and B, in the unit cell. The lattice vectors are: �� √3�� ,

√ � � , �� √3��

� ,√ � � where �� is the nearest neighbor distance, �� 1.42Å15

. Out of the four valence

electrons, three are used for �� bonds in carbon. The fourth electron is in a ��orbital, and there are two electrons per

unit cell in a ��orbital. Therefore, there are two orbitals, one for atom A, and one for atom B for a unit cell (there are two

�- bands, one for each electron). The tight-binding model Hamiltonian: Ĥ � ∑ ��ta� !,!"# �$%a��$%% + Hermitian

Conjugate (HC)16

can be expanded over the graphene unit cell site basis to obtain,

Ĥ � & '� tN) $,$′#

&e+,-∙$�e,-"∙$" / e,-∙$e,-∙0� / /e,-∙$e,-∙0�%a-� a�-′ / HC34

--"

heretrepresentsthetransferintegralcorrespondingtoelectronichoppingbetweenatomsandtheFourier-transformedcreationandannihilationoperatorsaredefinedas, a��$% �

√G∑ e+,H∙$- a-� ,a��$′% � √G∑ e+,HJ∙$′-J a�-J ,

Alternatively, thiscanbeexpressedinamatrixform, withanoveallphasefactorofe+,HJ∙�$+$"%, as Ĥ � ∑ �- a-� a�-� % ' 0 �tf�-%

�tf ∗�-% 0 ) a-a�-�, wheref�-% � Q1 / e,-∙�� / e,-∙��R. (1)

Figure 1. (a) Lattice structure of single layer graphene; Two carbon atoms per unit cell are labeled as 1, and 2 (grey, and

orange). Primitive vectors are �S, and�S�, (b) Lattice structure of bilayer graphene. Sub lattices for the lower layer are A1,

and B1, and those for the top layer are A2, and B2, with relative positions of atoms projected onto the x-y plane (c) Lattice

structure of twisted bilayer graphene for rotation θ, (d) tBLG θ=21.8°, with [(m,n)=(1,2)], highlighted unit cell for (e)

θ=9.4°, (f) θ=3.9°

The diagonal term HAA corresponds to the orbital interactions between two A atoms, HBB corresponds to the orbital

interactions between two B atoms. HAB, and HBA represent hopping between the two sites A, and B. To find the

dispersion relation, setting onsite energies, TU � TV � 0,and diagonalizing the Hamiltonian;

E��-% � t�f ∗�-%f�-% � t�Q1 / e+,-∙�� / e+,-∙��RQ1 / e,-∙�� / e,-∙��RE�-% � XtY3 / 2cos�- ∙ ��% / 2cos�- ∙ ��% / 2 cos�- ∙ �� %%,expressing in (x, y) components of k,



EQk[, k\R�Xt]1 / 4 cos '√ ^_`� ) cos ^_a� � / 4cos� ^_a� �,wherewith lattice constant a� √3��.

This well-known dispersion relation is illustrated graphically in Figure 2a. At Brillouin zone boundaries, the function

f(k) goes to zero.15

At K points, the solutions of the dispersion relation are degenerate giving zero bandgap between the

valence band, and conduction band. Near K points, the transfer Hamiltonian is like the Dirac Hamiltonian, and the

dispersion relation is approximately linear, which describes massless quasiparticles.2

2.2 Electronic band structure of bilayer graphene in the tight binding approximation

For AB stacked or Bernal bilayer graphene, there are interlayer 2pz orbital interactions between the atoms of the unit cell

of the upper layer (1) and lower layer (2). In Figure 1b we illustrate the lattice structure of bilayer graphene along with

the relative positions of atoms projected onto the x-y plane. In this bilayer structure, there are now clearly four distinct

atoms (A1, B1, A2, and B2). Their electronic coupling can be approximated by considering the intralayer contributions

(A1/B1, B1/B2), and the new nearest-neighbor interlayer contributions corresponding to A1/A2 and B1/B2 shown in

Figure 1b.16

Taking four distinct atoms into account (A1, B1, A2, B2) in the tight binding model, Castro et al. and Neto

et al. show that the Hamiltonian can be re-expressed as:

Ĥ � ��t% ∑ [a,� ,,c# b, / ac�bc / HC] � γ∑ [af�a, / HC] ,,f# / ε∑ [ac�ac / ,,c# bc�bc]18, 19

Here,T represents the onsite energies, -t� hij1|Ĥ|il1mis the intralayer transfer integral for electronic hopping

between A1 to B1, and A2 to B2 and -nrepresents the hopping between A1 to A2 (hφA1|Ĥ|φA2m%, and B1 to B2

(hφB1|Ĥ|φB2m%.

Using the Fourier transformed operators;a,��rS% � √G∑ e+,_qqS⋅!qSst_qqS a_qqS� ,b,��rS% � √G∑ e+,_qqS⋅!qSut_qqS b_qqS�, anddefiningvectors rSv, � RqqS,v,rS3, � RqqS,v / rSc, rSvf � RqqS,v / rSx it has been shown the approximate Hamiltonian for bilayer graphene is,Ĥ � ��t%∑ [e,_qqS⋅!qqSya_qqS� b_qqS /!qSy e,_qqS⋅!qqSya�_qqS� b�_qqS / e+,_qqS⋅!qqSyb_qqS� a_qqS / e+,_qqS⋅!qqSyb�_qqS� a�_qqS] � γ[e+,_qqS⋅!qSza�_qqS� a_qqS / e,_qqS⋅!qSza_qqS� a�_qqS] /ε[a_qqS� a_qqS / a�_qqS� a�_qqS / b_qqS� b_qqS / b�_qqS� b�_qqS];whichcanalternatelybeexpressedinmatrixformas, Ĥ � ∑ �kqS a1kqS† b1kqS† a2kqS† b2kqS† %}

~ εA1 �tf�-% �γ 0�tf∗�-% εB1 0 0�γ∗ 0 εA2 �tf�-%0 0 �tf∗�-% εB2 ��a1kqSb1kqSa2kqSb2kqS� (2)

Where, f�-% � e,-∙$� / e,-∙$� / e,-∙$� , and εv, ε3, εv�, andε3�are onsite energies on atomic sites A1, B1, A2, and B2

respectively. The nearest neighbor vectors are: $ � a� �√ , � , 0� , $� � a� �√ , � � , 0� , $ � a� � √ , 0, 0� , $x �b��0,0, 1%; giving f�-% � et�a��√� �et�`�� / e+t�`�� % / e+t�a��√� � et�a��√� 2cos�_`^�� % / e+t�a��√� .

The 2X2 blocks in the upper-left side and the lower-right side of the Hamiltonian in equation (2) represents the

intralayer coupling, which looks similar to the monolayer Hamiltonian terms. The 2X2 blocks in the upper-right side,

and the lower-left side of the Hamiltonian represents interlayer coupling, where the parameter γ describes the coupling

between orbitals A1, A2, and/or B1, B218

. The parameters γ � 0.14eV, t � 3.16eV, andεv, ε3, εv�, ε3� � 0in

equation (2) have been obtained using infrared spectroscopy20

. The well-known free electron band structure of AB

stacked bilayer graphene is roughly illustrated in the Figure 2b.

Without bias V, 2pz orbital interactions between four atomic sites are responsible for four bands in the dispersion relation

as shown in Figure 2c, two for the conduction band, and two for the valence band. The valence band pairs and

conduction band pairs are split by the amount of about 0.4 eV, which is an interlayer coupling energy. The splitting

occurs due to the strong bonding, and anti-bonding between atomic orbitals A1, A2, and/or B1, B2. The hopping

between A1, A2, and/or B1, B2 is responsible for low energy bands. The tight binding model is in good agreement with

DFT calculations in the low energy limit21, 22, 23

. Wang et al. showed that with a potential bias V between two layers of

graphene, it is further possible to see the shift in electrochemical potential between the layers32

.



layer A K

a nayer B

kX

(b) layer

A layer B (d)

i

íe'13

--',/ X

a

El

2.3 Effective free electron model: Electronic band structure of tBLG

Lastly, we complete our review of the free electron graphene models by considering of the structure of twisted bilayer

graphene defined by two layers of AA stacked bilayer graphene rotated around a common site by an arbitrary angle �. The two lattice vectors for AA stacked bilayer graphene with � � 0° are just� � a��1,0%and�� a� � , √ � �. For

non-zero angles the lattice vectors are more complicated because they must span the new superlattice, and are given

stacking angle indexed vectors; � � �� , and�� .25 Rotation angle θ � 0° produces AA stacked bilayer

graphene and � � 60°corresponds to AB bilayer graphene stacking.

Figure 2. (a) Representation of the band structure for single layer graphene. (b) tBLG free electron band-structure, (c) the

band dispersion near the K-point in bilayer graphene, (d) cross-sectional view of tBLG shows vHS transitions X13, X24

between avoided crossing regions.

Rotation angle � and – � produce a similar band structure. tBLG does not have a periodic structure in general because of

mismatch between the uniformity of layers with respect to each other. The structure is periodic only for some special

angles with a well-defined unit cell. A periodic lattice structure of tBLG for rotation angles � � 21.8°, and� � 9.4°, � �3.9° is shown in Figure 1d, e and f. When the rotation angle is small, the interference between two lattice vectors in

two layers gives rise to the pattern called the ‘Moiré pattern’25, 26

. The unit cell is relatively big for small rotation angles

as seen in Figures 1e and f. The lattice vectors for a given angle are: � � m� / n�� ; �forlayer1%, ; �forlayer2% �� R� � � and the lattice constant is L � |L| � |L�| � |�+�|^��,��%; where m, n are integers.24

For electronic states near the Fermi level, only pz orbitals needs to be taken into account in the tight binding model. For

twisted bilayer graphene, neighbors are rotated with respect to each other (unlike Bernal AB stacking). Therefore, we

now have to consider both the pp� and the pp� terms to account for the new interlayer interactions between atomic

orbitals. As shown by Shallcross et al.24,25

, the Hamiltonian can be written as,

Ĥ � ��1%∑ tQR,�RcR�R, �� Rc� ,,c# / HC (3)



Resonant exciton

\ xs-X13+X24

if Fano Resonance

_/, '7---\ , Fano Resonance

Ene

rgy r' X N w

XA=X13 -X24

Bound exciton('ghost' state)

where, tQR,�RcRisthetransferintegral. The transfer integral matrix equations for each type of interlayer orbital

interactions are given by: V � � �γ�e¡¢+ £��, andV ¤ � γe¡¥+ £�� 26, with the ratio

¡¥^� � ¡¢^� . Where, a�is the

nearest neighbor distance, ais the interlayer distance, d is the distance between two orbitals, γ�is the transfer integral

between nearest neighbors, and γis the transfer integral between nearest neighbor atoms that are located vertically.

Combining these terms, the combined transfer integral is �tQR,�RcR � V � ¦1 � §Q¨t+¨yR⋅©ª «�¬ / V ¤ §Q¨t+¨yR⋅©ª «�with, a� 0.14nm, a 3.35Å, d 0.335nm, γ� 2.7eV, γ 0.48eV, asobtainedfromliterature26.Using theabove transfer integral, thedispersion relationcanbeobtainedfromthedeterminantoftheHamiltonianofequation�3%.13Aroughillustrationoftheresultingfreeelectroninterlayerbandstructureof tBLGisshowninFigure2b.There isananti-crossingwherebandsoftwolayersmeet.Thisanti-crossingisaresultofinterlayerinteractionsbetweenthelayers.Figure 2d sketches the cross-section view of the band structure, showing the van Hove Singularity (vHS) transitions X13

and X24.The bands near K, and K′ come from single layer graphene (layer 1, and layer 2), and they are folded into the

same Brillouin zone. These bands don’t mix with each other giving rise to the linear dispersion relation near K, and K′. Near the M point, there is a splitting in energy due to anti-crossing of the bands. The allowed optical transitions are also

shown. The band structure of tBLG for different rotation angles look similar, however, the overall energy decreases by

minimizing the rotation angle. The splitting energy near the M-point is of the order of interlayer coupling between the

two layers, which is about 0.2 eV for all possible rotation angles.15

For rotation angles � 1°, parabolic dispersion is

obtained. For rotation angles around 1°, there bands are flat near the Fermi level. There is a transition from parabolic to

linear dispersion for rotation angles 1° ´ � ´ 2°. For angles above 10° and up to the symmetric point of 30°, the

dispersion is linear as in single layer graphene at the K point27

.

2.4 Review of bound exciton model for tBLG

Upon photoexcitation of tBLG, exciton effects may manifest themselves owing to Coulombic interactions of e-h pairs.

To theoretically model the many-body excitonic effects, it is necessary to solve the BSE as shown by Rohlfing et al.28

: �µ¶· � µ¸·%j¸¶·¹ / ∑ hº»¼|½¾¿|º′»′¼′mj¸"¶"·"¹ � À¹¸J¶J·J j¸¶·¹ , where, j¸¶·¹ is the exciton wave function in k-space, À¹is

the exciton eigenenergy,½¾¿is the e-h interaction kernel, and |º¼m, |»¼m are the hole and electron states, respectively. In

order to predict possible bound exciton states, it is important to know the e-h attractive energy µÁ¹, which roughly

corresponds to the binding energy, and recently the first-principle BSE simulations in Liang et al.14

reported that µÁ¹ � 0.5ÂÃ for 21.8o tBLG.

Figure 3. Upon resonant optical excitation, degenerate Fano resonance states X13 and X24 rehybridize producing a higher

energy resonant exciton state Xs and lower energy bound exciton state XA.



1 MHz AOM

modulator,

L<Pipiezo

1 n scanning mirror5

I

sample

scanningconfocalmicroscope

X

Specifically, Liang et al. solved for µÁ¹ � hÄ|½¾¿|Äm � ∑ �µ¶· � µ¸·%�j¸¶·¹ ��j¸¶·¹ � �¸¶· À¹, which is the net exciton

kinetic energy plus the weighted single-particle band energy difference between electrons and holes14

. To simplify the

direct analysis of the first principle BSE simulation, low-energy effective model is often further assumed, giving a

simpler perturbed Hamiltonian that is analogous to Equation (1), specfically29

; Å�¼% � 'Å��¼, 0% ÆÇÆ Å��¼ � ∆½, �%), with Å��¼, 0% � ћºÊ Ë 0 Â+ÌÍ�¼Î � Ï¼Ð%ÂÌÍ�¼Î / Ï¼Ð% 0 Ñ, where Æ � ∆ 0 11 0� (4)

The average interlayer interaction between AB and BA stacking order is described by matrix T with interlayer coupling

strength∆. The low-energy effective model is best for small-twisting angles because the linear Dirac-Fermion

dispersion is preserved. Using the BSE and the low effective model, Liang et al.14

found that upon resonant excitation of

tBLG, you can access degenerate Fano resonant transitions X13, X24 shown in Figure 2d which then effectively

rehybridize as depicted in Figure 3. The symmetric superposition of the two degenerate transitions give rise to a higher

energy bright state and anti-symmetric superposition give rise to the lower energy dark state (‘ghost’ state, see figure 3).

The constructive interference couples with the lower lying continuum which broadens the resulting resonant bright

excitonic state. The antisymmetric superposition cancels the coupling between the lower lying continuum making it a

localized bound excitonic state. The so-called ghost Fano resonance effect was found in quantum dot molecules.30

This

model is appropriate for small twist angle, however, the double resonance of transitions and the destructive interference

plays crucial role in existence of strongly bound excitons.14

The formation mechanism of this dark state XA is very

general, and may hold exciting promise for other twisted stacked 2D vdW materials.

3. EXPERIMENTAL

To experimentally test which model (sections 2.3 vs. 2.4) best describes the resonant excited state of tBLG best we

perform ultrafast microscopy measurements on single-grain of tBLG. We begin with multilayer graphene grown using

CVD method on copper foil and then transferred to silicon nitride grids, silicon or fused silica. Transient absorption

(TA) microscopy on tBLG requires (i) identification of large-area tBLG regions (ii) probe-beam diffraction limited

resolution TA. Single-grain regions of tBLG were identified using diffraction-limited scanning confocal TA microscopy

with 120 fs delayed pulses. tBLG regions were detected by exciting above resonance and probing well-below resonance

(typically at 0.8 eV). tBLG regions show a markedly enhanced TA when the resonance lies between the pump and probe

beam energies, owing to the strong electronic relaxation bottleneck effect in the interlayer tBLG states.

Figure 4. (a) Optical setup for transient absorption (TA) microscopy. Sub-diffaction limited pump, and probe pulses are

raster scanned , and the sample can be imaged against the laser noise floor by employing a lock-in amplifer detection

synched to an acousto-optical (AO) modulator (1 MHz), (b) Stacked TA images for a movie of the localized electronic

decay.



(a)

-wilFUn/ ntv 1.

3 v1 1.4,t? 4

xs+p 1UU N

Xs(bright)

ri io r=u..L p511' t=U. 4

1

-91.2-

LL

1337-fXA (dark)

Vjg

W

t=20 ps I X10 t =100 ps l120 µm(bi

0.0J .. S ground

0

orm

aliz

ed0

orc/

R, n

c

4mpl

itude

A

vw S

tBLG - bBir

bBLGIx-1 , intraband

1

cc

\ /..

. 1 n..h Mk

....\,.....f

-I N,,,,2 oh i .

0 50 100 150o

1.0 1.2 1.4 1.6 1.8 2.0 2.2Delay time (ps) Two photon transition energy (eV. 2xE )

After the regions with anomalous electronic relaxation dynamics are identified, the precise absorption resonances were

later measured using hyperspectral absorption imaging.31

By collecting the full-frame absorption movies, specific

absorption spectra can be acquired by integrating over a defined region, and plotting as a function of absorbing

wavelength. The correspondence between absorption resonance and twist angle has been previously established12,31

.

Once all optical measurements were complete, darkfield transmission electron microscopy (TEM) was used to determine

precise angle assignments and a composite image is constructed. Similar results were obtained for tBLG on silicon,

silicon nitride and fused silica substrates.

Scanning confocal ultrafast transient absorption (TA) microscopy enables us to simultaneously obtain near diffraction-

limited spatial resolution while also have sub-time resolution. This enabled us to study the electron relaxation dynamics

in single-grain of graphene. In Figure 3a and 3b, we show bilayer CVD graphene locally excited with a modulated (1

MHz) 140 fs pump pulse at 980 nm. We then probe graphene at 1650 nm using a second collinear probe pulse at some

time-delay, t. By collecting the change in reflectance (∆R(t)) of the probe pulse we plot the dynamics of graphene in both

space and time. By stacking the frames in Figure 3b, we can reconstruct a ‘movie’ of photoexcited hot electrons

relaxing. This electron-relaxation ‘movie’ is also a novel fast imaging technique for nanomaterials, and requires only

seconds to acquire each frame.

Figure 5 a. Transient Absorption (TA) microscopy maps at each time-delay show a greatly enhanced, long-lived electronic

population localized to the 6.8° tBLG grain shown. Video 1 shows resonantly pumped and probed tBLG showing strong evidence of an electron relaxation bottleneck in the vicinity of the expected avoided crossing van Hove singularity optical

resonances (http://dx.doi.org/10.1117/12.2262003). b. Comparative TA relaxation kinetics of resonantly excited tBLG (orange), bBLG (gray), (6,5) SWCNTs, and few layer WSe2. c. Bound exciton model d. Two-photon TA spectrum of 8°tBLG, showing higher lying state at 1.82 eV and lower lying state at 1.12 eV (blue). One-photon absorption spectrum (orange) subtracted from the absorptive contribution of Bernal bilayer graphene.



4. RESULTS AND DISCUSSION

When two sheets of graphene stack, the interlayer electronic states hybridize, resulting in a prominent visible absorption

peak that is tunable with the stacking angle. Recent first principle Bethe-Salpeter simulations of twisted bilayer

graphene, predict that interlayer electronic orbitals interfere destructively to form stable, strongly bound exciton states32

.

While this excitonic model corroborates the experimental absorption line shape observed33

, the actual existence of

strongly- bound excitons in an otherwise metallic system remains controversial and untested.

To test these conflicting models

34, we use one and two-photon confocal scanning transient absorption (TA) microscopy

as an incisive space-time probe of both the tBLG interlayer state energies and electronic population. Figure 5

unambiguously demonstrates the existence of manifold of bright and dark interlayer states that create a critical energy

relaxation bottleneck in resonantly excited tBLG. As shown in Figure 5a, upon resonant excitation at t=0.1 ps, we

observe a strong positive signed interband transient response from tBLG grain. By contrast, the surrounding Bernal

stacked bilayer graphene (bBLG) gives a comparatively weak the weak negative signed intraband contribution to the

transient optical conductivity. The roughly bi-exponential decay may be comparable to known excitonic systems like

single-walled carbon nanotube (SWCNT). However as shown in Figure 5d, tBLG relaxation kinetics are highly

dissimilar from bBLG and show a distinct relaxation bottleneck. One and two-photon TA spectrum of tBLG 8° domain is

shown in Figure 5d showing one state above and one below (blue) the bright state resonance (orange). These results

support recent theory13

outlined in section 2.4 that advocate for strongly bound, stable excitons in tBLG. Specifically, it

shows a strongly-bound exciton model works best as evidenced by; i. the radically enhanced and long-lived electronic

population in Figure 5a, b, ii. bright/dark state asymmetry34

in Figure 5d, and

iii. rigorously enforced one- and two-

photon selection rules in Figures 5c-d. Collectively, this suggests that not unlike SWCNTs, tBLG electronic structure

may also be dominated by a low-lying, strongly-bound exciton state13,34,35

.

5. CONCLUSIONS

We have demonstrated how you can access different interlayer functionalities of vdW materials by stacking and twisting

two monolayers. Upon stacking two graphene sheets together in a minimum energy configuration, it is well known that

you obtain massive chiral quasiparticles with parabolic dispersion relation for low energy, and the bands touch at zero

energy. Our work concerns when you have two sheets of graphene stacked at angle θ. In this twisted configuration, the

velocity of photoexcited electrons can change as a function of the rotation angle owing to an avoided crossing region that

creates interlayer electronic states. For the free-electron band structure model, these avoided crossing regions give vHs-

like resonances that have been known since 200932

to resonantly enhance the optical ~20% oscillator strength. In this

work, we consider how many body interactions become important in tBLG by presenting further evidence that is able to

form bound excitons.

Our ultrafast microscopy results lends experimental support to a theoretical model put forward by Liang et al.14

that

predicts that bound excitons occur from a cancellation of exciton-continuum coupling (often referred to as a ‘ghost’ Fano

resonance effect). Our transient absorption microscopy was able to ‘film’ the journey of electrons once photoexcited at

the tBLG resonances. The high population and long carrier relaxation in tBLG is strikingly different than AB stacked

BLG, suggesting some of the resonantly excited carriers are not coupled to the lower lying continuum sates. We referred

to this observation as an electron relaxation bottleneck that can be best explained by the existence of a lower lying state

located at 0.37 eV below the bright state resonance for 8.7o tBLG domain. In our model, the photoexcited carriers can

populate a symmetrically hybridized interlayer exciton state by 1-photon resonant excitation. Subsequently, these

excitons relax impulsively to the bound antisymmetric strongly-bound exciton state that is optically dark to 1-photon

excitation. Our results support that such states are weakly coupled to the continuum, forming a quasi-stable exciton with

an appreciable lifetime. These new experimental observations provide new evidence to support recently works33,34

that

suggests tBLG is a novel van der Waals material where free electrons can co-exist with bound excitons upon resonant

excitation. The growing evidence for this double resonance picture creating bound interlayer excitons is very general

and may hold exciting promise for other stacked, twisted 2D vdW materials. Control over the stacking and twisting of

2D vdW materials offers a new degree of freedom that is inaccessible with traditional 3D bulk materials. For tBLG, the

collective preliminary research suggests exciting applications for fast photosensitive devices requiring both stable

excitons and hybrid metallic properties.



ACKNOWLEDGMENTS

This research work was supported in part by a grant from the Spectroscopy Society of Pittsburgh, Oregon BEST and

ONAMI. Material fabrication was supported by Cornell’s AFOSR (FA 9550-10-1-0410) grant. We thank Li Yang at

University of Washington, St. Louis for helpful discussions.

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ultrafast microscopy captures the dynamics of bound...

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